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Although joint angle is commonly computed from the coordinates of the joint centers as a user-angle (see the User-Angle Issues section for the details), it can be also computed from the relative orientation angles of the joint. In 1-DOF joints such as the hinge joint, the joint angle corresponds to one of the orientation angles and no additional computation is required. But in joints with more than 1 DOF, additional computation must be performed to obtain the joint angle. From [6] of Computation of the Orientation Angles:
where TD/P = the transformation
matrix from the proximal reference frame to the distal reference frame at a
joint, and
and
where s = the unit vector of a segment's longitudinal axis. As one can see in [3], the
longitudinal axis vector of the distal segment described in the proximal
reference frame has nothing to do with angle
Thus, the joint angle
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© Young-Hoo Kwon, 1998- |
,
[1]
= the relative orientation angles between the segments at the joint. Now, let's assume that the
Z axes of the segmental
reference frames coincide with their respective longitudinal axes of the
segments:
,
[2]
,
[3]
because it is the rotation angle about the Z axis. The angle between the
longitudinal axes of the proximal and distal segments forming a joint (
)
can be computed from the scalar product of the two s vectors: from [2]
and [3],
.
[4]
is
.
[5]